dogsleep

Light or fitful sleep; a nap that is easily interrupted.

This was Gabriel Varden's state as, nodding in his dog sleep, and leaving his horse to pursue a road with which he was well acquainted, he got over the ground unconsciously, and drew nearer and nearer home.

[M]any of the convicts made up for their lack of rest by snatching a dog-sleep in the bared bunks.

Feigned sleep.

Juvenal, indeed, mentions a drowsy husband, who raised an estate by snoring, but then he is represented to have slept what the common people call dog's sleep